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Plant available water in saline soils--revisited.


Applications of Groenevelt et al.'s (2004) theory have evaluated both plant response and drainage effects on the calculation of plant available water in saline soils (e.g. Shani et al. 2007; Asgarzadeh et al. 2014; Mohammadi and Khataar 2018) and inserted them into user-friendly software (e.g. de Lima et al. 2016). In the present paper we offer a more elegant model for the water retention curve, [theta](h), and outline two alternative ways to attenuate the differential water capacity for osmotic stress, along with a dimensionless sensitivity factor, to account for the differing tolerance of plants to saline conditions.

Groenevelt et al. (2004) presented a dimensionless weighting function to account for osmotic stress in calculating plant available water in saline soils using the integral water capacity, 1WC ([m.sup.3] [m.sup.-3]). The osmotic weighting function, [[omega].sub.o](h) took the form:

[[omega].sub.o](h) [equivalent to] [[1 + [partial derivative][h.sub.o]/ [partial derivative]h].sup.-1] (1)

in which [partial derivative][h.sub.o]/[partial derivative]h represents the incremental change in the osmotic head, [h.sub.o] (m) per unit change in the matric head, h (m). Here, the notation is altered to include partial differentials rather than ordinary differentials, to acknowledge that all other factors influencing soil water availability are held constant and can be dealt with separately. The IWC originally outlined by Groenevelt et al. (2001) is therefore more correctly written:

[mathematical expression not reproducible] (2)

in which [theta] is the volumetric water content ([m.sup.3] [m.sup.-3]), [partial derivative][theta]/[partial derivative]h is the differential water capacity, C(h) ([m.sup.3] solution, [m.sup.-3] bulk soil, [m.sup.-1] matric head), and where the [[omega].sub.i](h) are multiplicative, dimensionless weighting functions of the matric head, h (m), that attenuate C(h) before integration.

As the initial salt concentration (and [h.sub.o]) in the saturated soil increase during drying, the weighting function described in Eqn 1 causes attenuation of C(h) and thus reduces the overall magnitude of the IWC. The shape of the weighting function illustrated in fig. 7a and b of Groenevelt et al. (2004) seemed perplexing at the time because although it declined from unity at saturation, where the salt concentration was most dilute, it subsequently increased back towards unity with increasing matric head even though the salt concentration increased and the soil was still relatively wet.

We have since observed other shapes of weighting functions arising from Eqn 1 for different soils, and we are convinced a rational physical explanation must exist. To understand and justify the nature of such a weighting function that decreases or increases (or does both) during drying, we consider the following three idealised examples:

Example 1. Plant seedlings (previously acclimatised) are placed in pots of well-aerated salt solutions of various concentration (held constant somehow) ranging from very dilute up to a solution having [h.sub.o] = 150 m (the so-called 'wilting point').

Example 2. Plant seedlings are placed in the same type of pots described in Example (1) but first soil is placed in the pots and subsequently kept saturated with the same (constant) well-aerated salt concentrations.

Example 3. Plant seedlings are placed in one of the soil pots described in Example (2) - e.g. with [h.sub.o]= 10 m, just less than 'saline'--and no drainage or evaporation is allowed; all water therefore leaves the pot of soil by transpiration alone, such that the salt concentration gradually increases as the water content decreases.

In Example 1, plants readily extract water and nutrients from the most dilute solutions and thereby grow well. Assuming root cell membranes have a reflection coefficient of 1.0 (i.e. little or no salt enters the plant) a graduated negative growth response is seen with increasing salt concentration such that plants in solutions approaching [h.sub.o] = 150 m wilt and die due to intolerable osmotic and ion toxicity stresses (c.f. Rengasamy 2010); this scenario was demonstrated by Magistad et al. (1943). The same or similar occurs in Example 2: plants show a graduated negative response to increasing osmotic stress in pots (Niu et al. 2010) but where the matric head is close to saturation (e.g. Schmidhalter and Oertli 1991) the soil matrix plays little role in restricting water availability - all plant responses come entirely from osmotic stresses or ion toxicities. In Example 3, by contrast (and assuming soil aeration is non-limiting), plants initially extract water and nutrients easily from the soil. However, as more water is removed, the salt concentration and osmotic head increase during drying, so soil water extraction gradually becomes more difficult and requires more energy (Ayers et al. 1943). Here a combined negative growth response occurs as both the osmotic and matric heads increase (Bernstein 1974; Kateiji et al. 1998). However, although the effects of matric and osmotic stresses have been shown to be roughly similar per unit head (e.g. Wadleigh and Ayers 1945; Shalhevet and Hsiao 1986), the changes in these heads are not linearly related to each other and it can be argued that the soil matric head may be more important per unit head than the osmotic head (e.g. Schmidhalter and Oertli 1991; Groenevelt et al. 2004; Kiani and Abbasi 2009). For this reason, as the water content declines by say half, the salt concentration and osmotic head double in magnitude, whereas the matric head (depending on the water retention curve) may increase by orders of magnitude. Thus the greatest effects of osmotic stress occur where the greatest reductions in water content occur (because this is where the largest increase in salt concentration occurs), whereas the greatest effects of the soil matrix occur where the matric head increases most rapidly (depending on the shape of the water retention curve). Salinity effects in coarse-textured soils are thus generally more severe and can set-in at smaller matric heads than they do in finer textured soils (Butcher et al. 2018).

We therefore contend that (1) a weighting function is required to attenuate the differential water capacity for the effects of osmotic stress on plant available water and (2) although a weighting function must always be <1.0, it need not always follow a monotonic decline from 1.0 down to 0. In essence the weighting function is derived from a combination of the initial salt concentration plus the water retention curve itself, so there are many possible shapes for such functions.

Assumptions and boundary conditions

Here we consider a closed system in static condition in which salts are preserved (i.e. no drainage and no root uptake of salt) this is a reasonable assumption for most saline, alkaline and sodic soils, where drainage is rather poor (Bernstein 1974; Rengasamy 1987) but even some drainage can be accommodated. The saturated state is typically deemed to be a relevant starting point (Bernstein 1974) although it is arguable that other slightly drier points (e.g. 'field capacity') may be more suitable, particularly when free drainage removes significant quantities of water and solutes. Regardless, the concentration of salt at saturation and field capacity is similar, after which the solute system can be considered closed for practical purposes. This means that the product of the volumetric water content ([m.sup.3] solution [m.sup.-3] bulk soil) and the concentration of salt (mole salt [m.sup.-3] solution) is constant - this is the mass balance. The mass balance implies that we cannot, at this stage at least, deal with the developments by, for example, Homaee et al. (2002) or Mohammadi and Khataar (2018), in which open systems are required. Indeed, when experimental data eventually arise, they may show that more than one osmotic weighting function is required to accommodate multiple different situations (e.g. where the reflection coefficient of plant cells is <1 and osmo-regulation must be accounted for). In such cases, the above fundamental principles must be abandoned to accommodate a more intuitive weighting, for which experimental verification will be necessary. At present, however, the lack of experimental evidence limits further progress along dynamic lines.

In the mass balance, the concentration of salt is replaced by the osmotic pressure according to Van't Hoff s law (see below), which leads to the relation that uses easily defined and measured or calculated parameters (after Richards 1954):

[[theta].sub.s] [h.sub.os] = [theta](h) [h.sub.o](h) (3)

where [[theta].sub.s] ([m.sup.3] [m.sup.-3]) is the directly measured (or indirectly calculated) saturated volumetric water content; [h.sub.os] (m) is the indirectly measured osmotic head of the saturated soil; [theta](h) is the directly measured unsaturated volumetric water content as a function of the matric head, h (m); and [h.sub.o](h) is the osmotic head of the unsaturated soil expressed in terms of the matric head (m). Frequently [h.sub.o] is approximated from data compiled by Campbell et al. (1949) and summarised after Richards (1954) as [absolute value of [h.sub.o]] = 3.6 ECS, where ECS is the electrical conductivity of a saturated soil paste extract (dS [m.sup.-1]).

Eqn 3 is more of an 'energy balance' than a 'mass balance' and its origin lies in Van't Hoff s equation: [pi] = nRTc, where tt is osmotic pressure (Pa), n is the degree of dissociation (dimensionless), R is the gas constant (J [mole.sup.-1] [K.sup.-1]), T is temperature (K) and c is the concentration of solutes (mole [m.sup.-3]). As for the Ideal Gas Law, Van't Hoff s equation is accurate only for dilute solutions. Eqn 3 is based on fundamental principles that do not require experimental verification here, so developments based on this equation (c.f. Approach 7, below) also do not require experimental verification, although experimental data are always welcome and interesting.

We also assume here that most economically important plants take up no significant quantity of salt (i.e. solute reflection coefficient close to unity; see Knipfer and Fricke 2010), and that permanent wilting occurs when the total soil matric plus osmotic head, [h.sub.t], reaches 150 m:

[[[h.sub.t]].sub.wilt] [equivalent to] [[h+[h.sub.o]].sub.wilt] = [[h.sub.wilt] + [h.sub.o,wilt]] = 150 m (4)

When no salt is present, the lower boundary of soil water availability is controlled simply by the soil matric head, [h.sub.wilt] = 150 m. When salt is present, however, the matric head at wilting, [h.sub.wilt], is determined from Eqn 3, which can be rearranged to solve for the (more difficult to measure) osmotic head in terms of the matric head, [h.sub.o](h):

[h.sub.o](h) = [[theta].sub.s][h.sub.os]/[theta](h) (5)

Water retention curve and calculating where wilting occurs

The model of the volumetric water retention curve used here was defined by Grant et al. (2010), which uses an 'anchor point' ([[theta].sub.a], [h.sub.a]):

[theta](h) = [[theta].sub.a] + [k.sub.1]{exp [- [([k.sub.0]/[h.sub.a]).sup.n] - exp [- [([k.sub.0]/h).sup.n]]} (6)

in which [k.sub.l] and n are dimensionless fitting parameters and [k.sub.0] is a fitting parameter with the dimension length and appropriate units (e.g. m). We note here that in Groenevelt et al. (2004) the coefficient, n, appeared inside the inner brackets of the argument of the exponential. By placing it outside these brackets, we make the contents of the inner brackets dimensionless. The fitting parameter, [k.sub.0], thus takes the dimension of length and can be considered a characteristic pore length of the porous medium. The magnitude of [k.sub.0] obtained from curve fitting is now different from the one obtained using the earlier notation of Groenevelt et al. (2004). Anchoring the water retention curve at the point of saturation, [[theta].sub.a] = [[theta].sub.s] and [h.sub.a] [right arrow] 0 m, reduces Eqn 6 to:

[theta](h) = [[theta].sub.s] -[k.sub.1]{exp[-[([k.sub.0]/h).sup.n]]} (7)

An interesting aspect of the water retention curve described by Eqn 7 is that when it is plotted on a semi-log scale its inflection point is located at the matric head, [h.sub.ip] = [k.sub.0] (Grant and Groenevelt 2015).

Substituting the water retention curve of Eqn 7 into Eqn 5 produces the relation:

[h.sub.o](h) = [[theta].sub.s][h.sub.os]/ [[theta].sub.s] - [k.sub.1] {exp[-[([k.sub.0]/h).sup.n]]} (8)

which can be plotted for a range of different soil textures and different initial salt conditions representing a practical range of salinity faced by economically important crops, say between E[C.sub.S]= 4 dS [m.sup.-1] (Fig. la) and 10 dS m 1 (Fig. 1 b). A red dashed line is inserted to illustrate where the lines for each soil cross the limiting total head of [h.sub.t] = 150 m, and the corresponding matric and osmotic heads at wilting are shown in Table 1. In Fig. la and b, the region below the red dashed line can be considered to represent combinations of the osmotic and matric heads in which plants can extract water from the soil, while the region above the red dashed line represents combinations in which plants cannot extract soil water. The osmotic stress caused by salinity is more severe in lighter than in heavier textured soils (Figs 1 a and b) (i.e. the sands intersect the line, h + [h.sub.o] = 150 m at smaller matric heads).

Fig. la and b can also be used to identify the volumetric water content at which plants may wilt permanently, [[theta].sub.wilt]. Actually, [[theta].sub.wilt] can be calculated directly from the water retention curve plus knowledge of [h.sub.os] using the relation:

[[theta].sub.wilt] = [[theta].sub.s] - [k.sub.1]{exp [-[([k.sub.0]/150 - [h.sub.o][(h).sub.wilt]).sup.n]]} (9)

or by substitution of Eqn 3 into Eqn 9 we get:

[[theta].sub.wilt] = [[theta].sub.s] - [k.sub.1]{ exp [-[([k.sub.0]/150 - ([h.sub.os][[theta].sub.s]/ [[theta].sub.wilt]).sup.n]]} (10)

In Eqn 10, [[theta].sub.wilt], appears implicitly (i.e. on both sides of the equation) but all other parameters are taken from the water retention curve (Eqn 7) and the osmotic head of the saturated soil paste extract (from the measured electrical conductivity). A 'root' function (a numerical iterative procedure) in any mathematical software package can therefore be used to produce the water content at which wilting occurs for different values of [h.sub.os]. The following analytical solution can also be used to achieve the numerical result produced by Eqn 10; the only difference is that the axes need to be reversed to plot the result:

[h.sub.os] ([[theta].sub.wilt]) = [[theta].sub.wilt]/ [[theta].sub.s]{150 - [k.sub.0][[-ln(([[theta].sub.s] - [[theta].sub.wilt])/[k.sub.1])].sup.-1/n]} (11)

Fig. 2 shows the numerical result (i.e. Eqn 10) of precisely what one would expect: for zero salt at saturation, lighter texture soils (e.g. coarse sand, fine sand and fine sandy loam) have lower water contents at wilting point than soils with greater clay contents (e.g. sandy clay loam and basin clay). For increasing amounts of salt at saturation, the water content at wilting increases. That some of the lines intersect can also be expected, and arises simply from the nature of their respective pore size distributions, reflected in the water retention curves.

Depending on the field instrumentation available, [h.sub.wilt] may be of greater interest than the corresponding volumetric water content. The value of [h.sub.wilt] can be determined either numerically or analytically. For a numerical result, an implicit relation for [h.sub.wilt], is first prepared from Eqns 7 and 10; then solutions for [h.sub.wilt] for different [h.sub.os] are determined numerically, as above:

[[theta].sub.s] h[o.sub.s]/150 - [h.sub.wilt] = [[theta].sub.s] - [k.sub.1]{exp (-[([k.sub.0]/[h.sub.wilt]).sup.n])} (12)

The same result for [h.sub.wilt] can also be determined analytically (then plotted with reversed axes) using the relation:

[h.sub.os]([h.sub.wilt]) = [[theta].sub.s] - [k.sub.1]exp[-[([k.sub.0]/[h.sub.wilt]).sup.n]]/ [[theta].sub.s] x {150 - [k.sub.0][[-ln[[[theta].sub.s] - ([[theta].sub.s] - [k.sub.1] exp(- [([k.sub.0]/[h.sub.wilt]).sup.n]))]/[k.sub.1]].sup.-1/n]} (13)

Numerically determined examples of how [h.sub.wilt] behaves for varying [h.sub.os] in the same five soils are shown in Fig. 3. As expected, for zero salt at saturation, wilting occurs for all five soils at [h.sub.wilt] = 150 m; and declines with increasing osmotic head at saturation. Although there is no particular reason to truncate the lines in Figs 2 and 3, we stopped at [h.sub.os] = 75 m because this is already well beyond the range of salt concentrations of practical interest in mainstream irrigated agriculture (i.e. 14.4 m < [h.sub.os] < 36 m, or 4 dS [m.sup.-1] < [EC.sub.S] < 10 dS [m.sup.-1]).

Two approaches to attenuate C(h) for osmotic stress

Approach 1

We first present the weighting function of Eqn 1 for each soil texture at low and high osmotic heads in the saturated soil (Fig. 4a and b). These figures illustrate greater initial weighting for the sands than fortheheaviertexturedsoils(compare curves 1 and5in Fig. 4a and b). The figures also illustrate greater overall weighting for the higher initial osmotic head than for the lower initial osmotic head (compare Fig. 4a with 4b). All weighting functions decline relatively rapidly from saturation towards a minimum then rise again asymptotically towards unity.

The location of the minimum value of the weighting functions is of interest in interpreting the severity of weighting caused by the interactions between different water retention curves and the increase in salt concentration during drying. The location of the minimum value of the weighting function depends on soil texture and lies between two significant matric heads: the matric head at maximum differential water capacity, [h.sub.max], and the matric head at the inflection point of the water retention curve plotted on semi-log axes, [h.sub.ip]. The [h.sub.max] at the maximum differential water capacity, C(h), occurs at:

[h.sub.max] = [k.sub.0] [(n+1/n).sup.-1/n] (14)

while [h.sub.ip] of the water retention curve, [theta](h), occurs at:

[h.sub.ip] = [k.sub.0] (15)

Table 2 shows that, for the coarsest textured soil (coarse sand), the minimum value of the weighting function occurs at a matric head close to that at the inflection point of the water retention curve, [h.sub.ip] or [k.sub.0]. For the two slightly finer textured soils (fine sand and fine sandy loam), the minimum lies somewhere between [h.sub.ip] and [h.sub.max]. For the heavier textured soils (sandy clay loam and basin clay), the minimum of the weighting function coincides more closely with [h.sub.max]. Further evidence from a larger number of soils is required to evaluate the veracity of the textural link here but the location of the minimum value of the weighting function appears to have some dependence on the shape of the water retention curve through the inflection point as well as the maximum differential water capacity.

Approach 2

We now offer an alternative (and perhaps simpler) weighting function based on the idea that when no salt is present in the saturated soil, [[omega].sub.o](h) has a value of 1.0 (i.e. no weighting) and that when there is enough salt in the saturated soil to cause wilting even before the soil begins to dry (i.e. [h.sub.os] = 150 m), 0)o(h) has a value of zero (i.e. complete weighting). To construct such a function we simply subtract from unity the ratio of the osmotic head in the soil solution relative to the maximum total head that plants can cope with:

[[omega].sub.o] (h) [equivalent to] 1 -[h.sub.o](h)/150 (16)

in which [h.sub.o](h) is defined above.

The result of Eqn 16 is shown in Fig. 5a and b for the same soils and initial salt concentrations used for the other figures. Readers may find this approach more intuitively pleasing than that outlined in Eqn 1 because the weighting function declines monotonically from a maximum value [less than or equal to] 1.0 depending upon the initial salt concentration, and does not rise again. However, it should be noted that Eqn 16 does not yet have a theoretical basis in physics, chemistry or plant physiology - it is simply a logical construct at present.

The two approaches for attenuating the differential water capacity are compared in Table 3 for the five soil textures; the classical plant available water (PAW, [m.sup.3] [m.sup.-3]) is included as an unweighted reference for the IWC ([m.sup.3] [m.sup.-3]). As might be expected, the IWCs are all less than the PAWs, and of course the attenuation of available water is greater when the initial salt concentration is greater (c.f. upper practical limit values in Table 3). Also, there are clear textural effects, showing that weighting for osmotic stress reduces available water in the coarse sand by 95-100% relative to PAW values, whereas for the same conditions in basin clay, the reduction of available water is only 13-31% depending on the weighting approach adopted. The result of Approach 2 (Eqn 16) is generally less severe than that of Approach 1 (Eqn 1) although the magnitude of the differences between the two approaches decreases in heavier textured and more saline soils.

A plant-sensitivity factor, f, for osmotic stress

We leave it to the reader to choose the most suitable approach for a given situation but it is important to realise the two approaches are fundamentally different in nature: Approach 1 is based on physical and chemical principles that require a salt balance; and Approach 2 is simply an intuitively logical idea, which will require empirical evidence and evaluation. It is possible, for example, that if young seedlings of certain crops are transplanted from glasshouse situations having high-quality irrigation water in field situations irrigated with relatively saline water, they will respond negatively and immediately; this would call for weighting by Approach 1 (rapid attenuation of the water capacity at small matric heads followed by a reduction in attenuation as the soil dries out). If those same seedlings, by contrast, were germinated and grown to transplanting stage using the field irrigation water, they might respond less negatively or severely in the first instance but then decline slowly thereafter; this would call for weighting by Approach 2 (less severe initial attenuation followed by a steady attenuation as the soil dries out).

Regardless of the approach chosen, an additional modification can also be used to allow greater or lesser attenuation according to plant sensitivity to salinity. For example, Approach 1 (Eqn 1) can be adjusted using a dimensionless plant-sensitivity coefficient, [xi] as follows:

[[omega].sub.o]1(h) [equivalent to] [[1 + [xi](partial derivative][h.sub.o]/[partial derivative])].sup.1] (17)

The values of [xi] could be classed, for example, in three general categories: 1 < [xi] <10 for plants highly sensitive to salinity (e.g. 'halophobes'), 0.1 < [xi] <1 for plants moderately sensitive (e.g. glycophytes) and 0 < [xi] <0.1 for salt-insensitive plants (e.g. halophytesandxerophytes).Similarly,Approach2(Eqn I6)canbe adjusted using the same plant-sensitivity coefficient, as follows:

[[omega].sub.o]2(h) [equivalent to] 1-[xi] ([h.sub.o](h)/150) (18)

Fig. 6a and b shows how E influences the weighting from Approaches 1 and 2 for the coarse sand and the basin clay (other textures fall roughly in between). The boundaries for [xi], of course, have not been investigated for different plants, but a useful starting point would be to consider the groups suggested in Maas and Hoffman (1977) and Shannon and Grieve (1998). At present, however, the values of E should only be regarded as indicative until glasshouse and field experiments with different soils, plants and salinities provide more realistic guidance.


We have shown here that weighting the differential water capacity for osmotic stress in different soils can be achieved using at least two (very different) approaches and that a plantsensitivity factor can be invoked to modify the resulting attenuation for different plant species. Approach 1 is based on fundamental physical and chemical principles, and Approach 2 is more empirical and requires experimental evaluation under controlled conditions and eventually in the field. In this regard, we suggest that the simplicity and flexibility of our models, particularly when combined with the more elegant form of the Groenevelt-Grant equation presented here, may be of use in the evaluation and models to predict plant performance of various crops being screened in the field for genetic tolerance to salt stress in different soils (e.g. Munns et al. 2006; Toderich et al. 2018).

Conflicts of interest

The authors declare no conflicts of interest.


The Australian Water Recycling Centre of Excellence supported this collaborative research, which we dedicate to our late friend and mentor, Professor Beverly David Kay (University of Guelph). Bev worked tirelessly throughout his career to encourage and support students and colleagues to undertake strategic research using fundamental principles of the scientific method. We also acknowledge valuable conversations with Dr Robert S Murray (University of Adelaide) during the preparation of this manuscript; Eqn 16 was his creation.


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Handling Editor: Freeman Cook

C. D. Grant (ID) (A,C) and P. H. Croenevelt (B)

(A) School of Agriculture, Food and Wine, University of Adelaide, Waite Campus, PMB 1 Glen Osmond, SA 5064, Australia.

(B) School of Environmental Sciences, University of Guelph, Guelph, Ontario, Canada NIG 2W1.

(C) Corresponding author. Email:

Caption: Fig. 1. Osmotic head ([h.sub.o]) as a function of the matric head (h) for five soils of different texture (Rijtema 1969) having an osmotic head in the saturated paste extract of (a) [h.sub.os] = 14.4 m, equivalent to [EC.sub.S] = 4 dS [m.sup.-1] and (b) [h.sub.os] = 36 m, equivalent to [EC.sub.S] = 10 dS [m.sup.-1]. The dashed red line represents the limiting sum of the matric and osmotic heads, h + [h.sub.o] = 150 m.

Caption: Fig. 2. Volumetric water content at which wilting occurs. [[theta].sub.wilt], for different osmotic heads in the saturated paste extract, [h.sub.os], calculated numerically from Eqn 10 for five different soils (Rijtema 1969).

Caption: Fig. 3. Matric head at which wilting occurs, [h.sub.wilt], for different osmotic heads in the saturated paste extract, [h.sub.os], calculated numerically from Eqn 12 for five different soils (Rijtema 1969).

Caption: Fig. 4. Weighting functions based on Eqn 1 for saturated paste extracts (a) [EC.sub.S] = 4 dS [m.sup.-1] ([h.sub.os] = 14.4 m) and (b) [EC.sub.S] = 10 dS [m.sup.-1] ([h.sub.os] = 36 m), for soils of different texture: 1, coarse sand; 2, fine sand; 3, fine sandy loam; 4, sandy clay loam; and 5, basin clay (Rijtema 1969).

Caption: Fig. 5. Weighting functions based on Eqn 16 for saturated paste extracts (a) [EC.sub.S] = 4 dS [m.sup.-1] ([h.sub.os] = 14.4 m) and (b) [EC.sub.S] = 10dS[m.sup.-1] ([h.sub.os] = 36m), for soils of different texture: 1, coarse sand; 2, fine sand; 3, fine sandy loam; 4, sandy clay loam; and 5, basin clay (Rijtema 1969).

Caption: Fig. 6. Osmotic weighting functions for coarse sand (Rijtema soil 1) and basin clay (Rijtema soil 19) using (a) Approach 1 (Eqn 17) and (b) Approach 2 (Eqn 18) to apply a plant-sensitivity factor relevant to 'very sensitive' (0.01 [less than or equal to] [xi] [less than or equal to] 0.1), 'sensitive' (0.1 [less than or equal to] [xi] [less than or equal to] 1) and 'tolerant' (1 [less than or equal to] [xi] [less than or equal to] 10) crops for [h.sub.os] = 14.4 m (ECS = 4 dS [m.sup.-1]).
Table 1. Final matric head, h, osmotic head, [h.sub.o], and total head,
[h.sub.t], at wilting for two different initial (saturated) osmotic
heads (and corresponding electrical conductivities, EC) for five
different soil textures. The heads at wilting occur at the intersection
with the red dashed line in Fig. la and h, where h + [h.sub.o] = 150 m

                                             Final heads at wilting (m)

Soil texture            Initial osmotic        h     [h.sub.o]    K
(Rijtema No.)            head and EC at

Coarse sand (1)       [h.sub.os] = 14.4 m,    1.2      148.8     150
                      [EC.sub.s] = 4 dS
Fine sand (4)         [m.sup.-1]             56.3      93.7      150

Fine sandy                                   78.7      71.3      150
loam (11)

Sandy clay loam                              117.4     32.6      150

Basin clay (19)                              126.5     23.5      150

Coarse sand (1)       [h.sub.os] = 36.0 m,    0.3      149.7     150
                      [EC.sub.s] = 10 dS
Fine sand (4)         [m.sup.-1]              7.4      142.6     150

Fine sandy loam                              16.8      133.2     150

Sandy clay loam                              73.4      76.6      150

Basin clay (19)                              93.5      56.5      150

Table 2. Matric head (h, m) corresponding to the minimum value of
weighting function of Eqn 1 compared with [h.sub.ip] and [h.sub.max]
for five soils ranging from light to heavy texture (Rijtema 1969)

                Coarse   Fine       Fine        Sandy     Basin
                 sand    sand    sandy loam   clay loam   clay

[h.sub.ip] =    0.0744   0.676      1.43        3.50      51.8

h minimum       0.0831   0.365     0.888       0.00882    0.170

[h.sub.max]     0.0335   0.232     0.573       0.00836    0.160

Table 3. Comparative assessment of plant available water in five
soil textures (Rijtema 1969) calculated without weighting for
osmotic stress (PAW) and by weighting the differential water
capacity using two different approaches to calculate the integral
water capacity, IWC, at low and high initial salt concentrations

Lower and upper practical limits of salinity represented by
[h.sub.os] = 14.4 m ([EC.sub.S] = 4 dS [m.sup.-1]) and [h.sub.os] =
36 m ([EC.sub.S] = 10 dS [m.sup.-1]) respectively

                                           Lower practical limit

                                         IWC, [m.sup.3] [m.sup.-3]
                                         (% change) using Approach
                                                  1 or 2

Soil texture            PAW ([m.sup.3]    1. Eqn 1      2, Eqn 16
(Rijtema No.)            [m.sup.-3])
                         no weighting

Coarse sand (1)             0.033        0.002 (-95)   0.000 (-99)
Fine sand (4)               0.161        0.038 (-76)   0.111 (-31)
Fine sandy loam (11)        0.300        0.064 (-79)   0.122 (-59)
Sandy clay loam (14)        0.158        0.116 (-27)   0.132 (-16)
Basin clay (19)             0.191        0.167 (-13)   0.167 (-13)

                          Upper practical limit

                        IWC, [m.sup.3] [m.sup.-3]
                        (% change) using Approach
                                  1 or 2

Soil texture             1, Eqn 1      2, Eqn 16
(Rijtema No.)

Coarse sand (1)         0.001 (-98)   0.000 (-100)
Fine sand (4)           0.021 (-87)   0.047 (-71)
Fine sandy loam (11)    0.032 (-89)   0.062 (-79)
Sandy clay loam (14)    0.090 (-43)   0.094 (-41)
Basin clay (19)         0.143 (-25)   0.131 (-31)
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Author:Grant, C.D.; Croenevelt, P.H.
Publication:Soil Research
Article Type:Report
Date:May 1, 2019
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